Abstract
This contribution is concerned with a review of linearity axioms for fuzzy orderings with respect to three fundamental correspondences from the classical case - linearizability of partial orderings, intersection representation, and one-to-one correspondence between linearity and maximality. We obtain that it is virtually impossible to simultaneously preserve all these three properties in the fuzzy case. If we do not require a one-to-one correspondence between linearity and maximality, however, we obtain that an implication-based definition appears to constitute a sound compromise, in particular, if Lukasiewicz-type logics are considered.
| Original language | English |
|---|---|
| Title of host publication | Principles of Fuzzy Preference Modelling |
| Editors | B. De Baets and J. Fodor |
| Place of Publication | Gent |
| Publisher | Academia Press |
| Pages | 1-14 |
| Number of pages | 15 |
| ISBN (Print) | 90-382-0567-8 |
| Publication status | Published - 2003 |
Fields of science
- 101004 Biomathematics
- 101027 Dynamical systems
- 101028 Mathematical modelling
- 101029 Mathematical statistics
- 101014 Numerical mathematics
- 101015 Operations research
- 101016 Optimisation
- 101017 Game theory
- 101018 Statistics
- 101019 Stochastics
- 101024 Probability theory
- 101026 Time series analysis
- 102 Computer Sciences
- 102001 Artificial intelligence
- 102003 Image processing
- 102004 Bioinformatics
- 102013 Human-computer interaction
- 102018 Artificial neural networks
- 102019 Machine learning
- 103029 Statistical physics
- 106005 Bioinformatics
- 106007 Biostatistics
- 202017 Embedded systems
- 202035 Robotics
- 202036 Sensor systems
- 202037 Signal processing
- 305901 Computer-aided diagnosis and therapy
- 305905 Medical informatics
- 305907 Medical statistics
- 102032 Computational intelligence
- 102033 Data mining
- 101031 Approximation theory